A time series of Landsat 8 images at Gulf of Laganas, Zakynthos Island, Greece
Using the Panchromatic band for water column correction
to derive water depth and spectral bottom signature:
Landsat 8 OLIP bandset used for this work

Purple=1Blue=2Green=3PAN=4Red=5NIR=6 and SWIR1=7
Using pan sharpened images in this study
Pan sharpening  using Rstudio Brovey method

work done  november 2016

1 - NO NEED for field data, nor for atmospheric correction
2 - this is demonstrated in this website, using a variety of hyper/multi spectral data
Requirements are
1 - homogeneous water body and atmosphere
2 - some coverage of optically deep water
3 - some coverage of dry land
Problems are
1 - the precision on estimated depth is found wanting, because the noise-equivalent change in radiance  of accessible data is too high for shallow water column correction work 
2 - radiance data should be preprocessed by the provider at level 1 in order to improve S/N ratio
3 - exponential decay: the deeper/darker the bottom, the poorer the performances
I keep digging
until suitable data
become available
 GSD 15m pan-sharpened
The data

most variable atmosphere

TCC deglinted
  • Note the low Blue radiances along the western waterline of Zakynthos island: what's that?
  • This happens at various locations in this scene

Deglinting along Profile_Yellow

Glint regressions are excellent
Deglinting is excellent

Adjacency effect is fairly strong,
several kilometers wide


Calibration under RED ROI

Calibration Blue vs Green
  • Big star: brightest substrate is set to Coral Sand
  • BPL pixels: clearly display as a straight line
  • Reflectance of coral sand is ~2.7 times brighter than this bottom
  • Kblue/Kgreen=0.33  and   Kcoastal/Kgreen=0.35
    • this is Jerlov water type OI+0.9
    • this is very-very clear, just below OIA
  • Deepest bottom detection for this bottom: ~28 m
  • BUT deepest bottom detection for coral sand would be ~47 m
  • Shallowest pixels are at ~7.5 m
    • this sandy slope stretches from 7.5 m down to 28 m
  • Very few pixels in this ROI exhibit darker bottoms
  • Land pixels: they provide a clear view of the SOIL Line assumption
    • Lwcoastal~=26           Lacoastal ~=70
    • Lwblue   ~=20           Lablue     ~=47
    • Lwgreen ~=   2           Lagreen   ~=27
    • Lwpan     ~= 1.5          Lapan     ~=32

Calibration Coastal vs Green

Calibration Blue vs PAN

Calibration under BLUE ROI

Calibration Blue, Green, Red, NIR
  • Small crosses: I have added the BPL pixels of Red_ROI
  • Unchanged: calibration settings are unchanged
  • Identical: optical calibration for the water is quasi identical in both ROIs
  • Very dark: brightest bottoms at Red_ROI are three times brighter than at Blue_ROI
    • this makes for very dark sandy bottoms at Blue_ROI: only 1/8 of the brightness of coral sands!

Calibration Coastal, PAN, Red, and NIR


Ready for Modeling

Retrieved depth in centimeters
see full scene
see legend


B average bottom brightness

Insight on the uncertainty on fake depth over Land areas
In order to test 4SM against spectral variations of the bottom substrate,
I can enforce a depth over land to apply the water column attenuation from image calibration,
then process these "artificial shallow" pixels to see how well/bad this depth is retrieved.
Result of this exercise 
From very shallow to very deep, the algorithm yields a surprisingly good estimation of depth;
there is hardly any increase in uncertainty as depth increases.
But, wait: this does not include the quantization noise (mmm...)!
I tried including 8_bits quantization of the computation of "artificial" pixels:
absolutely NO change either of av_Z4SM or std_Z4SM for Zland=20m.
GSD=15 m, pan-sharpened. NO smoothing applied.
Just the estimated depth is "noisy", as an expression of
  • the reductive assumption on the Soil Line.
  • the pansharpening process : co-registration MULTI/PAN.
PAN solution
I suppose that this good result is in part a marked benefit of using the PAN band.
Add heterogeneous atmosphere/water
This does not account for the effect of the natural variations of the water/atmosphere optical properties,
which can be very nasty in their own right, and increase dramatically deeper than ~half of the shallow depth range.
Profile Land A along the beach
Profile Land B through town

Profile Land_C through agriculture
Depth applied to land pixels
ZLand=  1 m

ZLand=  2 m
ZLand=  5 m
ZLand=10 m
ZLand=15 m
ZLand=20 m
ZLand=25 m
ZLand=30 m
Average depth retrieved for three profiles
  0.97+-0.20 m...........N=1124
  1.93+-0.23 m
  4.83+-0.40 m
  9.56+-0.47 m
14.43+-0.47 m
19.34+-0.47 m
24.16+-0.40 m
29.01+-0.27 m.............N=553
Zland=1 m==>0.97+-0.2m
Zland=2 m==>1.93+-0.23m
Zland=5 m==>4.83+-0.4m
Zland=10 m==>9.56+-0.47 m
Zland=15 m==>14.43+-0.47m
Zland=20 m==>19.34+-0.47m